# If the radius of the earth’s orbit around the sun is 150 million kilometers, what is the speed of the earth in its orbit in kilometers per hour ?

Jun 6, 2018

I tried this:

#### Explanation:

We can use some relationships from Kinematics (rotational and linear):

1) linear ($v$) and angular ($\omega$) velocity are related as:

$v = \omega r$

2) angular velocity is the circumference described in time or:

$\omega = \frac{2 \pi}{T}$

where $T$ is the Period or time for an entire ($2 \pi$ radians) orbit.

In our case: $T = 1 \text{year} = 365 \cdot 24 = 8760 h$

so $\omega = \frac{2 \cdot 3.14}{8760} r a d \frac{\setminus}{h}$

so that:

$v = \omega r = \frac{2 \cdot 3.14}{8760} \cdot 150 \times {10}^{6} = 1.07 \times {10}^{5} k m \frac{\setminus}{h}$